# Lesson Worksheet: Binomial Theorem: Using Partial Fractions Mathematics

In this worksheet, we will practice decomposing rational expressions into partial fractions, then expanding them using the binomial theorem.

**Q1: **

By decomposing into partial fractions, find the quadratic approximation of and state the range of values of for which the approximation is valid.

- A,.
- B, .
- C, .
- D, .
- E, .

**Q2: **

By decomposing into partial fractions, find the cubic approximation of and state the range of values of for which the approximation is valid.

- A,
- B,
- C,
- D,
- E,

**Q3: **

By expressing in partial fractions, find the cubic expansion of and state the range of values of for which the approximation is valid.

- A,
- B,
- C,
- D,
- E,

**Q4: **

By expressing in partial fractions, find the quadratic approximation of and state the range of values of for which the approximation is valid.

- A,
- B,
- C,
- D,
- E,

**Q5: **

By writing in the form , find the expansion of up to the term and state the values of for which the expansion is valid.

- A,
- B,
- C,
- D,
- E,

**Q6: **

By decomposing into partial fractions, find the quadratic approximation of and state the range of values of for which the approximation is valid.

- A,
- B,
- C,
- D,
- E,

**Q7: **

By writing in the form , find the expansion of up to the term and state the values of for which the expansion is valid.

- A,
- B,
- C,
- D,
- E,

**Q8: **

By writing in the form , find the expansion of up to the term and state the values of for which the expansion is valid.

- A,
- B,
- C,
- D,
- E,

Find the percentage error in using approximation to estimate the value of , giving your answer to 2 decimal places.

**Q9: **

By decomposing into partial fractions, find the expansion of up to the term and state the values of for which the expansion is valid.

- A,
- B,
- C,
- D,
- E,

Find the percentage error in using approximation to estimate the value of .

**Q10: **

By decomposing into partial fractions, find the expansion of up to the term and state the values of for which the expansion is valid.

- A,
- B,
- C,
- D,
- E,

Find the percentage error in using the approximation to estimate the value of , giving your answer to one decimal place.